Solve for $x$ and $y$ using elimination. ${-6x+3y = 0}$ ${-5x+y = -6}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-3$ ${-6x+3y = 0}$ $15x-3y = 18$ Add the top and bottom equations together. $9x = 18$ $\dfrac{9x}{{9}} = \dfrac{18}{{9}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {-6x+3y = 0}\thinspace$ to find $y$ ${-6}{(2)}{ + 3y = 0}$ $-12+3y = 0$ $-12{+12} + 3y = 0{+12}$ $3y = 12$ $\dfrac{3y}{{3}} = \dfrac{12}{{3}}$ ${y = 4}$ You can also plug ${x = 2}$ into $\thinspace {-5x+y = -6}\thinspace$ and get the same answer for $y$ : ${-5}{(2)}{ + y = -6}$ ${y = 4}$